Question: Solve for $x$ and $y$ using elimination. ${-4x-y = -41}$ ${3x+2y = 37}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ ${-8x-2y = -82}$ $3x+2y = 37$ Add the top and bottom equations together. $-5x = -45$ $\dfrac{-5x}{{-5}} = \dfrac{-45}{{-5}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-4x-y = -41}\thinspace$ to find $y$ ${-4}{(9)}{ - y = -41}$ $-36-y = -41$ $-36{+36} - y = -41{+36}$ $-y = -5$ $\dfrac{-y}{{-1}} = \dfrac{-5}{{-1}}$ ${y = 5}$ You can also plug ${x = 9}$ into $\thinspace {3x+2y = 37}\thinspace$ and get the same answer for $y$ : ${3}{(9)}{ + 2y = 37}$ ${y = 5}$